After completing NG+, you will be able to go to a third playthrough, which doesn’t add anything but an optional superboss. This boss will be found via one of four different portals throughout the overworld, where it will suck in a random character for a one-on-one fight. Defeat the boss and that character will gain access to their ultimate weapon.
These four locations are as follows:
Black Tortoise Crevasse (near giant crater)
Near Militesi Capital in Azurr region
Near royal palace in Rilochy Province
The locations start with the first and will repeat themselves in the order listed. There doesn't appear to be a known method to the portals first spawning, but they can appear as soon as Chapter 4, whenever you are at the Deserted House for Free Time 4.2.